I wonder if Lewis, Gilbert and Booger would even give a **** about this one???? Image Unavailable, Please Login
I'm not going to read this whole thread. And I haven't taken a math class or a physics class in about 35 years. But as long as the diameter of the airplane TIRE is greater than the diameter of the airplane WHEEL, than the airplane will move forward from a fixed starting point, no matter how far the belt (which is moving at WHEEL speed) moves in the opposite direction. The rolling circumference of the tire is greater than the rolling circumference of the wheel. Hence the tire moves forward farther than the belt moves backwards, in the same amount of time. As the wheel accelerates, the speed of the tire increases in relation to the opposite speed of the belt. Right? Wrong?
THE FOCKING TREADMILL WILL OVERSPEED ITSELF APART AS SOON AS THE WHEELS TURN EVEN A LITTLE. I'm gonna switch it up here and make YOU tell ME why :0) And the plane will still take off. And Johnny 'big' L. will score with the hot stewardess. What a stupid question.
discussing wheel and tire dia? Are you even responding to the right question? uhhh it's so far beyond wrong it took me a minute to even justify replying.
Uh, the QUESTION, as posed in post #1, specifically says "the speed of the wheels". That's the question I was trying to answer. If it said "the speed of the tires" that changes the fixed part of the equation. Ta ta.
[Arnold Horshack]Ooh! Ooh! Mr Kotter, Mr Kotter! I wanna change my answer!!!![/Arnold Horshack] Yeah, I realised this when I woke up this morning. My analysis last night assumed that the friction force between the wheel and the belt couls easily be transmitted to the airplane, and it can, but it has to go through the wheel bearings, so the wheels would have to be spinning REALLY fast. At some point the tires wouldn't have enough grip and would start sliding on the belt, which is what I said last night, BUT: it's the power of the conveyor, not the plane, that will break the tires' traction by spinning them so fast. If the coefficient of friction was infinite and the bearings were frictionless, the belt speed and the wheel speed would go to infinity in an infinitesimal time. So: the plane only has to overcome bearing friction at the wheel speed at which the tire friction reaches its maximum and starts sliding against the belt. I'll have to think about whether that is better or worse for the airplane. Look out, there may be more pictures! Things like this make a person realise he's a complete nerd! Cos this is fun!
The plane will fly for one of two reasons: As so many have pointed out - correctly - the thrust from the engines has nothing to do with the rotational speed of the wheels. It is the thrust of the engine that pushes the plane forward, all the conveyor belt will do is cause the wheels to overspeed. If the conveyor belt can run so quickly that the engines thrust equals the drag caused by wheel bearing friction then the plane will still fly, even though it is standing still. Why? Well, at that point, through laminar attachment, the whipping belt will be generating sufficient head wind to make the plane lift off and hover in ground effects. Once off the belt wheel bearing friction will drop to zero and the plane will accelerate forward. If every time the plane lifted off, the conveyer belt would instantly stop running, then the plane would take off after a series of bounces. As an aside there have been a few postings on this thread explaining how an aircraft flies, quoting learned tombs and invoking Bernoullis principal. Actually most of the flying is done because of the angle of attack of the planes wing. Lots of aircraft, like Pitts specials, have symmetrical wings, indeed all helicopters have symmetrical wings, and, as observed, they fly. Wing shape can create lift, but angle of attack is the boy you need to actually get anywhere.
I think part of the confusion here is that there are two different version of the problem floating around: one says the belt goes the same speed as the plane, one says same as the wheels. Two different problems. The first one is simple, the second one is trickier. Yes the belt would be really "flying" to create enough drag in the bearings to equal the max friction between the tire and belt, but when you get one of these silly hypotheticals that's where the answer takes you: the wheels explode from spinning so fast and THEN the plane takes off! Anyone remember the one about the train traveling past the station platform at 99% of teh speed of light when forked lightning strikes both ends of the train? That one is fun too.....
ok. what was the question posed HERE? yes, yes i do. that was just as not fun in 4th grade as this is now. edit: that one is up there in my mind as the day our teacher told us (on april 1st) that ALL (yes ALL) systems were converting to metric. hmm, calendars, bra sizes... is there anything else????
Lock the wheels and make sure the plane has a powerful engine. The wheels will not rotate, and thus the treadmill will not move. The plane will skid to the end of the treadmill, with wheels locked (still no rotation), and take off. You have satisfied all points in the scenario, and the plae is flying. This is just like if you had a car on a treadmill going 70 mph. The car isn't going anywhere, right? Lock up the brakes (the treadmill will do the same), and your car will slide forward at 140 mph off the edge of the treadmill. Or if you aren't allowed to use the brakes... Since the thrust from the engine propells the plane forward (not the wheels), how is the treadmill going to put an equal and opposite force on the plane to keep it from moving? All the treadmill can do is spin the wheels, and no matter how fast you spin the wheels, no matter what direction you spin them, they will not move the rest of the plane (nor prevent it from moving), because they aren't applying a directional force - only a rotational force.
It doesn't matter how fast or slow the treadmill is moving or which direction it's turning. It doesn't even have to match the airplanes speed. You can have it going at 1000mph and the plane will still take off in the same distance. Go to an airport and use one of those luggage carts on the flat conveyor belts (the ones people stand on, not the ones that carry luggage). Put the cart on the conveyor and stand off the conveyor on the side of it. You control where it goes as long as you are holding onto it (engines on). Once you let go (engines off), the conveyor controls it.
try harder. i covered this in post #10. (first page!) if you want to go into that then it's beyond the reasonable parameters of the question. NOT if the treadmill EXACLTY compensates for the speed/acceleration of thewheels. try again. yes children, we are now beyond the current capabilities of technology. read the question again. sigh.... if the treadmill EXACTLY matches the speed of the wheels as stated in the query, then your theory is useless. forget HOW it happens, we don't care, that's not the question. PEOPLE!!!!!!!!!!!!!!! the question is can the plane take off? no. it CANNOT. the plane CANNOT move forwards. any more instruction required?????????
I guess you've never tried the shopping/luggage cart on a people mover (flat conveyor) at the airport. I dont' see how you can't realize it doesn't matter which way the wheels are turning or at what speed as long as an external force is applied (me applying the force while off the conveyor same as a jet engine). Edit: Go to the airport and rent one of those things. Stand on the side of the conveyor, but have the cart on the conveyor. Hold onto the cart and run as fast as you can down the entire conveyor and time yourself. Do this again, but with the cart off of the conveyor. The times will be the same if you ran the same speed in both trials.
I can't believe you people are getting 15 pages deep in a flawed question. Let's ask another question, then: If the aircraft cannot take off because the conveyor negates the wheel speed of the aircraft, ... ... then how does the aircraft move forward when the wheels are off the ground and not moving at all? And how does a seaplane take off with no wheels at all? Or try this: If your aircraft had a Vr of 50 knots and you had 60 knots of wind from the front of the aircraft, what would be the conveyor speed at take off? I weep for the public school system.
Exactly! I said almost the exact same thing http://www.ferrarichat.com/forum/showpost.php?p=135395242&postcount=33
Rather than wade through the pages of 'speculation' from apparent non-physicists, let's go for the short form answer: yes of course it will fly. The mention of wheels is a red herring. The purposes of wheels on an aircraft are: steering, braking, holding the aircraft above the earth's surface when at rest or when aircraft lift < aircraft weight. The acceleration of aircraft is strictly due to engine output. In the case of a jet, the momentum of the heated fuel/air mass hurled behind provide for an equal and opposite force upon the aircraft. All the moving runway will achieve in this scenario is to reduce the admittedly small force of wheel and tire friction from the total aircraft drag equation. It would make much more sense to temporarily attach the aircraft to the moving runway. The moving runway would better serve as a supplement to engine thrust for faster, safer, and more fuel efficient takeoffs, much in the same way the steam catapult on an aircraft carrier imparts additional momentum to the hapless F/A-18 trying to take off from a VERY SHORT runway. I bet that both Navy pilots and physicists have got this one nailed down.
Wow - I've been out all day and I come back to find we're up to a whopping 15 pages. I really don't understand why this problem has to be dressed up in some of the super-complex ways people have been doing. Answer me this: if a wheel is rolling down the road (whether on a plane or a car) and the car/plane is doing 100mph relative to the road, how fast is the wheel going? 100mph. How fast is it rotating? Depends on the size of the wheel, but that's irrelevant to this problem - the wheel is travelling forwards at 100mph. Then, if someone places a treadmill between the wheel and the road, and the wheel is still being pushed forwards (relative to the Earth) at 100 mph, the **rotational** speed of the wheel can be altered to anything you like. If the treadmill is doing 100mph forwards in relation to the Earth, the wheel isn't spinning at all, and if the treadmill is doing 100mph backwards in relation to the Earth, the wheel is still moving forwards at 100mph but is spinning as though it was doing 200mph (because its contact patch is connected to the treadmill). The whole crux of the problem is that the plane doesn't drive itself forwards (relative to the Earth and the still air) using its wheels - it just uses its engines to pull at the air and shoot the exhaust gases out the back. Look at the problem statement - for the conveyor belt to move backwards AT ALL, the plane has to have some FORWARD SPEED - the speed of the wheels. I'm sipping Margerita's with the other chaps, having arrived in the Caribbean after a pleasant flight. No Denial-juice for me!! (nice one ) Cheers! Rich
Haha.. This is quite interesting indeed. The solution is rather simple. The thrust of the jet engines is NOT independent of the rotation of the wheels which is in turn in contact with the large "treadmill". An airplane has to gain enough forward momentum in order to equal or exceed the wind speed in the opposite direction so that it generates lift--literally. Under normal circumstances, the jet engines give thrust which is delivered to the ground (which is still--relative to us) through the wheels, creating friction and causing movement in a certain direction--forward in most cases. In this case, when the "ground" itself moves and equals the speed of the wheels but in the opposite direction, as aforementioned, it is essentially frictionless. Therefore, the engines by itself does not make a plane take off...by giving thrust and "putting" that power through the wheels is how it gains momentum from 0-velocity to equal that of the wind speed (which is in the opposite direction) to create lift. Therefore, the plane CANNOT take off in the traditional manner. Ideally, if the plane was super-hi tech, it could turn the jet engines (fighter jet like the one Lockheed Martin has developed) downward and give it thrust making the plane take off straight up. It is all vectoral--the wind, wheel rotation, and thrust.
